Change the exponential statement 5^x=125 into an equivalent logarithmic statement.
I know the answer is log5(125)=(x)
Just don't know the steps to get it.
recall the basic definition of the logarithm:
b^(logb(x)) = x
logb(b^x) = x
5^x = 125
so, just take log5 of both sides:
log5(5^x) = log5(125)
x = log5(125)
To change the exponential statement 5^x=125 into an equivalent logarithmic statement, you need to understand the relationship between logarithms and exponents.
In general, the logarithm of a number to a certain base is the exponent to which the base must be raised to equal that number.
Now let's apply this concept to convert the given exponential statement into a logarithmic statement.
Step 1: Identify the base of the exponent. In this case, the base is 5.
Step 2: Identify the result of the exponent. In this case, the result is 125.
Step 3: Construct the logarithmic statement using the base and result identified in the previous steps.
The logarithmic form of the exponential statement 5^x=125 is log5(125) = x.
Explanation:
The base of the logarithm (in this case, 5) represents the number that is raised to a certain exponent.
The result of the logarithm (in this case, x) represents the exponent to which the base must be raised to obtain the given number (in this case, 125).
So, the logarithmic statement log5(125) = x is equivalent to the exponential statement 5^x=125.